We now claim that the vacuum current [Fig. REF (c)] is identical to the condensate current [Fig. REF (b)]. A simple principle that would give this result is that the current is fully determined by level energies and their occupations near the the Fermi surface, \(|E|\ll \Delta \) . The justification for this could be that leaving some unoccupied momentum levels deeper inside the Fermi surface would not lead to a state with low energy, and the full occupation of theres levels leads to cancelation of the contribution to current. Since the bound levels near the Fermi energy in the two cases, corresponding to Figs. REF (b) and (c) are identical with the same phase difference \(\phi \)  [1]}, [2]}, this principle leads to equal currents in the two cases.
